Why blender don't see my GPU
There are three reasons why you can't use the AMD Radeon HD 6770M for GPU rendering on your system:

GPU rendering on macOS with an AMD card isn't possible since Blender 2.80, due to the deprecation of the OpenCL compiler by Apple (see this answer for more information).
The GPU is below the minimum requirements for GPU rendering. The AMD Radeon HD 6770M has the TeraScale 2 micro-architecture, but GCN second generation or later is required on supported operating systems.
The GPU is below the minimum requirements for running Blender 2.8x. Only AMD graphics cards with GCN first generation or later are officially supported.

Therefore, the GPU is neither suited for GPU rendering nor running Blender 2.8x on any operating system. You may have to use an older version of Blender with lower minimum requirements.